Finite Group Databasebeta

← #30599269

Subgroups — #30599269

Order 15616.

554 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461546C212yesmaximal
2#21460695C212yesmaximal, complemented
3#21460695C212yesmaximal, complemented
4#382×D61C211yesmaximal, characteristic
5C2×#14519834—22no—
6C2×#14519832C2214yes—
7#16840628—22no—
8C2×C4⋊C4×D61C411yescharacteristic
9C2×C4⋊C4×D61C411yescharacteristic
10C2×C42×D61C2211yescharacteristic
11#16839628C411yescharacteristic
12#16839627C2211yescharacteristic
13#16839627C2211yescharacteristic
14#16839626—22no—
15#95×D61—22no—
16C61×#382C411yescharacteristic
17C22×#92420—24no—
18#14519834—28no—
19#14519832—28no—
20C22×C4×D61—21no—
21C22×C4×D61—21no—
22C22×C4×D61C2×C411yescharacteristic
23C22×C4×D61D412yes—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×#11758196—21no—
27C2×#11758196—21no—
28C4⋊C4×D61—42no—
29C4⋊C4×D61—42no—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61C2311yescharacteristic
32C42×D61—24no—
33#14519684—22no—
34#14519684—22no—
35#14519684—22no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C42×C61C2×C411yescharacteristic
39#95×C61—22no—
40C23×D61C22⋊C411yescharacteristic
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61C22⋊C412yes—
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—21no—
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C2×D412yes—
49C2×C4×D61—22no—
50C2×C4×D61—22no—
51C2×C4×D61—22no—
52C2×C4×D61—24no—
53C2×C4×D61—24no—
54C2×C4×D61—42no—
55C2×C4×D61—44no—
56C2×C4×D61—42no—
57C2×C4×D61—42no—
58C2×C4×D61—44no—
59C2×#92420—28no—
60C2×#92420—44no—
61C2×#92420—44no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61—22no—
65C4⋊Dic61—41no—
66C4⋊Dic61—41no—
67#11758196—42no—
68#11758196—42no—
69C4×Dic61—24no—
70C4×Dic61#4114yes—
71C23×C61C2×C22⋊C411yescharacteristic
72C22×D61—21no—
73C22×D61—21no—
74C22×D61—22no—
75C22×D61#10012yes—
76C22×D61#10414yes—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61#11712yes—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61#10112yes—
96C2×Dic61#12314yes—
97C4×D61—28no—
98C4×D61—48no—
99C4×D61—84no—
100C4×D61—84no—
101#92420—48no—
102#8718—611nomaximal, Sylow
103C22×C61#38111yescharacteristic
104C22×C61C2×#10011yescharacteristic
105C22×C61C2×#10111yescharacteristic
106C22×C61C2×#10412yes—
107C22×C61#42112yes—
108C2×D61—22no—
109C2×D61—24no—
110C2×D61—24no—
111C2×D61—22no—
112C2×D61#32914yes—
113C4×C61—22no—
114C4×C61—42no—
115C4×C61—81no—
116C4×C61—81no—
117Dic61—22no—
118Dic61—24no—
119Dic61—81no—
120Dic61—81no—
121C2×#382—611no—
122#1749—612no—
123#1295—612no—
124#1295—612no—
125C2×C61C2×#32911yescharacteristic
126C2×C61#152812yes—
127C2×C61#153311yescharacteristic
128C2×C61#182111yescharacteristic
129C2×C61#182612yes—
130D61—24no—
131C22×C4⋊C4—611no—
132C22×C4⋊C4—611no—
133C22×C42—611no—
134C2×C22⋊C8—1222no—
135C2×#97—614no—
136#382—611no—
137#382—611no—
138#382—611no—
139#382—1222no—
140#382#692311yescharacteristic
141C2×#95—1222no—
142#336—1222no—
143C61#871811yescharacteristic, complemented, Sylow
144C23×C4—611no—
145C23×C4—612no—
146C23×C4—1221no—
147C23×C4—1221no—
148C22×C8—1224no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—1221no—
152C2×C4⋊C4—1221no—
153C2×C4⋊C4—2442no—
154C2×C4⋊C4—2442no—
155C2×C4⋊C4C2×#692311yescharacteristic
156C2×C4⋊C4C2×#692311yescharacteristic
157C2×C42—611no—
158C2×C42—612no—
159C2×C42—1224no—
160C2×C42C2×#692311yescharacteristic
161C22⋊C8—1228no—
162#97—1228no—
163#95—22no—
164#95—1222no—
165#95—1222no—
166#95—1222no—
167C24—611no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—612no—
171C22×C4—611no—
172C22×C4—1222no—
173C22×C4—1224no—
174C22×C4—1222no—
175C22×C4—1224no—
176C22×C4—1222no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—2442no—
180C22×C4—2442no—
181C22×C4—2442no—
182C22×C4—2444no—
183C22×C4—2444no—
184C22×C4C22⋊#692312yes—
185C22×C4C22×#692311yescharacteristic
186C2×C8—1228no—
187C2×C8—2444no—
188C2×C8—2444no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—2441no—
192C4⋊C4—2441no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C42—22no—
196C42—614no—
197C42—1224no—
198C23—612no—
199C23—614no—
200C23—1221no—
201C23—1221no—
202C23—1222no—
203C23C2×C22⋊#692311yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—614no—
214C2×C4—612no—
215C2×C4—1228no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—4884no—
221C2×C4—4884no—
222C2×C4—2448no—
223C2×C4—2441no—
224C2×C4—2441no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4#1451985612yes—
228C8—2448no—
229C22—614no—
230C22—1224no—
231C22—1222no—
232C22—1222no—
233C22—1224no—
234C22#1684070511yescharacteristic
235C22D61⋊#10011yescharacteristic
236C22D61⋊#10111yescharacteristic
237C22D61⋊#10412yes—
238C22#1684075912yes—
239C4—22no—
240C4—42no—
241C4—81no—
242C4—81no—
243C4—1222no—
244C4—1224no—
245C4—4881no—
246C4—4881no—
247C2—1224no—
248C2D61⋊#32911yescharacteristic
249C2#2146128212yes—
250C2#2146129911yescharacteristic
251C2#2146171911yescharacteristic
252C2#2146172712yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#8718
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21460695C2semidirect
3. #21460695C2semidirect
143. C61#8718semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214615462
#214606952
#382×D612
#871861